Problem: Simplify the following expression: $r = \dfrac{a^2 - 3a - 70}{a - 10} $
First factor the polynomial in the numerator. $ a^2 - 3a - 70 = (a - 10)(a + 7) $ So we can rewrite the expression as: $r = \dfrac{(a - 10)(a + 7)}{a - 10} $ We can divide the numerator and denominator by $(a - 10)$ on condition that $a \neq 10$ Therefore $r = a + 7; a \neq 10$